BH-NS MAGNETOSPHERE collaborator Masaru Shibata (YITP, AEI) - PowerPoint PPT Presentation

BH-NS MAGNETOSPHERE 和田知己 collaborator Masaru Shibata 
 (YITP, AEI) YITP (Tomoki Wada) 高エネルギー宇宙物理学研究会 2018

Binary Black Hole → GW150916, .. 5 detection Binary Neutron Star → GW170817 & GRB170817A, macronova, afterglow γ-ray Radio Electromagnetic Counterpart was detected !!! GW ASTRONOMY ∼

Binary Black Hole → GW150916, …5.5 detection Binary Neutron Star → GW170817 & GRB170817A, macronova, afterglow γ-ray Radio Electromagnetic Counterpart was detected !!! GW ASTRONOMY What can we detect with GW from BH-NS merger ??? ∼

What happens with BH-NS merger？ Typically ・light BH → tidal disruption … destroyed NS will light ・heavy BH → NO tidal disruption COUNTERPART WITH BH-NS MERGER Nothing will light ?? （Else） （ ） M BH / M NS ≲ 5, a ≳ 0.5

What happens with BH-NS merger？ Typically ・light BH → tidal disruption … destroyed NS will light ・heavy BH → NO tidal disruption COUNTERPART WITH BH-NS MERGER Nothing will light ?? （Else） （ ） NS … STRONG MAGNETIC FIELD → LIGHT EMISSION？ M BH / M NS ≲ 5, a ≳ 0.5

・assume pulsar is dipole ⃗ ⃗ パ LIGHT EMISSION R ⃗ ⃗ ・NS is conductor ⃗ ⃗ ⃗ ⃗ PULSAR MAGNETOSPHERE →. in coronation frame ・Poisson equation ・Electric field parallel to Magnetic field will accelerate charged particles ⃗ ⃗ B NS B out Ω × ⃗ E NS = − ( r ) B NS × c E = 0 E out ∼ Ω B NS R 5 cr 4 e − E out ∥ E out ∼ Ω R E out c B ∥ B NS B out

・assume pulsar is dipole ⃗ →THIS CAN BE COUNTERPART CHARGED PARTICLE WILL EMIT LIGHT IF THIS HAPPENS IN BH-NS BINARY, ⃗ ⃗ LIGHT EMISSION パ ⃗ ⃗ ⃗ R ・NS is conductor ⃗ OF GW FROM BH-NS MERGER ⃗ accelerate charged particles →. in coronation frame ・Poisson equation PULSAR MAGNETOSPHERE ・Electric field parallel to ⃗ Magnetic field will ⃗ B NS B out Ω × ⃗ E NS = − ( r ) B NS × c E = 0 E out ∼ Ω B NS R 5 cr 4 e − E out ∥ E out ∼ Ω R E out c B ∥ B NS B out

PROBLEM Pulsar … accelerates particles Does exist in binary ?? Setting Consider magnetic dipole rotating BH Is there which accelerate particles from NS ?? Calculate induced electric field パ E out ∥ E out ∥ E out ∥

AIM Pulsar magnetosphere Binary magnetosphere Assume NS is dipole which is spinning → Calculate induced electric field → will accelerate particles パ Assume NS is dipole which is rotating BH → Calculate induced electric field → is there ? E out ∥ E out ∥

BASIC EQUATIONS ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ Maxwell equations （ in flat spacetime ） ⃗ ⃗ Current is rotating dipole ⃗ ⃗ ⃗ ∂ t ∇ × B + E = 0 ∇ ⋅ B = 0 ∇ ⋅ E = 4 πρ ∂ t E − ∇ × B = − 4 π J m λμ ：magnetic moment x μ NS ( τ ) ：orbit of NS

：angular direction ：angular direction VECTOR HARMONICS EXPANSION Expand vector fields using vector harmonics Maxwell equations Time evolution equation party even party odd B lm B lm B lm B i 2 3 1 B lm 1 ：radial direction B lm 2 B lm 3

GREEN FUNCTION METHOD ・Fourier transformation Regular at outgoing wave at infinity ・give boundary condition Construct Green function & Solve equation r = 0 ω r h (1) ω r j l ( ω r ) l ( ω r ) r NS BH

MAGNETIC FIELD times vector harmonics & sum up l, m

ELECTRIC FIELD times vector harmonics sum up l, m

ELECTRIC FIELD times vector harmonics sum up l, m WHAT IS HAPPENING ????

NUMERICAL ELECTRIC(Z=0) 200 1000rEz0 150 r ⋅ E 100 @ constant time 2 π surface 50 Ω ∼ 60 / M 0 y separation -50 R = 5 -100 total mass -150 M tot = 10 M ⊙ -200 -200 -150 -100 -50 0 50 100 150 200 x / M

NUMERICAL ELECTRIC（ ） rE z=30 z=90 200 200 1000rEz30 1000rEz60 150 150 100 100 50 50 0 0 y y -50 -50 -100 -100 -150 -150 -200 -200 -200 -150 -100 -50 0 50 100 150 200 -200 -150 -100 -50 0 50 100 150 200 x x

NUMERICAL MAGNETIC ( ) r ⋅ B z=10 z=30 200 200 1000rBz10 1000rBz30 150 150 100 100 50 50 0 0 y y -50 -50 -100 -100 -150 -150 -200 -200 -200 -150 -100 -50 0 50 100 150 200 -200 -150 -100 -50 0 50 100 150 200 x x almost dipole dipole + spiral arm (radiation)

NUMERICAL MAGNETIC ( ) r ⋅ B z=10 z=30 200 200 1000rBz10 1000rBz30 150 150 dipole 100 100 dipole 50 50 0 0 y y radiative -50 -50 -100 -100 -150 -150 -200 -200 -200 -150 -100 -50 0 50 100 150 200 -200 -150 -100 -50 0 50 100 150 200 x x almost dipole dipole + spiral arm (radiation)

NUMERICAL MAGNETIC ∼ 2 π z=60 z=100 Ω 200 200 1000rBz60 1000rBz100 150 150 100 100 50 50 0 0 y y radiative -50 -50 radiative -100 -100 -150 -150 -200 -200 -200 -150 -100 -50 0 50 100 150 200 -200 -150 -100 -50 0 50 100 150 200 x x almost spiral arm (radiation) spiral arm (radiation)

PARTICLE ACCELERATION will happen Particle acceleration There is and IS THERE ?? E out ∥ 200 1 z10cos 10 50rE 150 5rB 100 0.5 5 50 cos 0 0 y -50 0 z -100 -0.5 -150 -5 -200 -1 -200 -150 -100-50 0 50 100 150 200 x 200 1 z60cos -10 0 5 10 15 20 150 x 100 0.5 50 cos E out 0 0 y ∥ -50 -100 -0.5 -150 -200 -1 -200 -150 -100-50 0 50 100 150 200

BINARY MAGNETOSPHERE magnetosphere can’t be vacuum and may filled with plasma.. There are gaps in co-rotating magnetosphere particle acceleration & charged particle emits light パ There is In binary, electromagnetic field changes dynamically → there must be many gaps E out ∥

PARTICLE ACCELERATION Order estimate of particle acceleration Plasma Considering only mode R r NS BH l = 1 ∼ m z Ω R ∼ v B ( R ) ρ ∼ E R 3 R E r ∼ m z Ω 2 R r 2

PARTICLE ACCELERATION Accelerating region Emitting area S ∼ R 2 R r NS BH ∼ m z Ω ρ ∼ E R ∼ v B ( R ) R acc ∼ Ω − 1 R 3 R E r ( r ) ∼ m z Ω 2 R r 2 L ∼ IV ∼ ( ρ cR 2 ) ⋅ ( E r ( R acc ) R acc ) ∼ ( m z ) 2 Ω 3 R − 1 ∝ R − 6 acc

Emitting area PARTICLE ACCELERATION cf. rotating dipole Accelerating region S ∼ R 2 R r NS BH R acc ∼ Ω − 1 L ∼ IV ∼ ( ρ cR 2 ) ⋅ ( E r ( R acc ) R acc ) ∼ ( m z ) 2 Ω 3 R − 1 ∝ R − 6 acc L ∼ ( m z ) 2 Ω 3 R − 1 acc ∼ 10 42 erg/s L ∼ ∝ R − 7

SUMMARY ・BH-NS binary … there is especially near binary → magnetosphere must filled with plasma ・charged particle may be accelerated → luminosity → it can be electromagnetic counterpart as precursor ・frequency ・evaluate acceleration ・effect of plasma ・effect of GR FUTURE WORK E out ∥ L ∼ 10 42 erg/s